ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  hbexd Structured version   GIF version

Theorem hbexd 1581
Description: Deduction form of bound-variable hypothesis builder hbex 1524. (Contributed by NM, 2-Jan-2002.)
Hypotheses
Ref Expression
hbexd.1 (φyφ)
hbexd.2 (φ → (ψxψ))
Assertion
Ref Expression
hbexd (φ → (yψxyψ))

Proof of Theorem hbexd
StepHypRef Expression
1 hbexd.1 . . 3 (φyφ)
2 hbexd.2 . . 3 (φ → (ψxψ))
31, 2eximdh 1499 . 2 (φ → (yψyxψ))
4 19.12 1552 . 2 (yxψxyψ)
53, 4syl6 29 1 (φ → (yψxyψ))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1240  wex 1378
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-ial 1424
This theorem depends on definitions:  df-bi 110
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator